Question

Rezolvați prin metoda reducerii sistemului:
b){x+5y+3=0
x-2y-4=0
c){2x+7y=3
4x-y=-9
d){3x-2y-9=0
x+y-8=0
dau coroana.....

Answer 1

$\left\{\begin{matrix} x + 5y + 3 = 0\\ x - 2y - 4 = 0\end{matrix}\right.$

$\left\{\begin{matrix} x + 5y = - 3 \: | \times ( - 1) \\ x - 2y = 4\end{matrix}\right.$

$\left\{\begin{matrix} - x - 5y = 3\\ x - 2y = 4\end{matrix}\right.$

$- 5y - 2y = 3 + 4$

$- 7y = 7 \: | \div ( -7 )$

$y = - 1$

$x - 2y = 4$

$x - 2 \times ( - 1) = 4$

$x + 2 = 4$

$x = 4 - 2$

$x = 2$

$\left\{\begin{matrix} 2x + 7y = 3\\ 4x - y = - 9 \: | \times 7 \end{matrix}\right.$

$\left\{\begin{matrix} 2x + 7y = 3\\ 28x - 7y = - 63\end{matrix}\right.$

$2x + 28x = 3 - 63$

$30x = - 60 \: | \div 30$

$x = - 2$

$4x - y = - 9$

$4 \times ( - 2) - y = - 9$

$- 8 - y = - 9$

$- y = - 9 + 8$

$- y = - 1 \: | \times ( - 1)$

$y = 1$

$\left\{\begin{matrix} 3x - 2y - 9=0 \\ x + y - 8 = 0\end{matrix}\right.$

$\left\{\begin{matrix} 3x - 2y = 9\\ x + y = 8 \: | \times 2 \end{matrix}\right.$

$\left\{\begin{matrix} 3x - 2y = 9\\ 2x + 2y = 16\end{matrix}\right.$

$3x + 2x = 9 + 16$

$5x = 25$

$x = \frac{25}{5}$

$x = 5$

$x + y = 8$

$5 + y = 8$

$y = 8 - 5$

$y = 3$